On Hele-Shaw models with surface tension
نویسندگان
چکیده
منابع مشابه
On Hele-shaw Models with Surface Tension
It is shown that surface tension effects on the free boundary have a regularizing effect for Hele-Shaw models, which implies existence and uniqueness of classical solutions for general initial domains.
متن کاملClassical solutions for Hele-Shaw models with surface tension
It is shown that surface tension effects on the free boundary are regularizing for Hele-Shaw models. This implies, in particular, existence and uniqueness of classical solutions for a large class of initial data. As a consequence, we give a rigorous proof of the fact that homogeneous Hele-Shaw flows with positive surface tension are volume preserving and area shrinking.
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Morphological instabilities are common to pattern formation problems such as the non-equilibrium growth of crystals and directional solidification. Very small perturbations caused by noise originate convoluted interfacial patterns when surface tension is small. The generic mechanisms in the formation of these complex patterns are present in the simpler problem of a Hele-Shaw interface. Amid thi...
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The experimental results of Saffman & Taylor (1958) and Pith (1980) on fingering in a Hele Shaw cell are modelled by two-dimensional potential flow with surface-tension effects included at the interface. Using free streamline techniques, the shape of the free surface is expressed rn the solution of a nonlinear integro-differential equation. The equation is solved numerically and the solutions a...
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This paper concerns global existence for arbitrary nonzero surface tension of bubbles in a Hele-Shaw cell that translate in the presence of a pressure gradient. When the cell width to bubble size is sufficiently large, we show that a unique steady translating near-circular bubble symmetric about the channel centerline exists, where the bubble translation speed in the laboratory frame is found a...
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ژورنال
عنوان ژورنال: Mathematical Research Letters
سال: 1996
ISSN: 1073-2780,1945-001X
DOI: 10.4310/mrl.1996.v3.n4.a5